Spectrum linewidth

Fig. 8 a Narrow emission spectrum (linewidth 0.7 meV) shifted by the 0-0 transition energy, exhibiting linearly polarised emission (P = 0.98) as shown in (c). b The broad emission spectrum (linewidth 2.40 meV) of a different single chain is only weakly linearly polarised (P = 0.33), (d). The dotted lines in c and d indicate the fluorescence background. Reprinted from [28]... 

Correlation function decay constant, spectrum linewidth... 

Due to the rather stringent requirements placed on the monochromator, a double or triple monocln-omator is typically employed. Because the vibrational frequencies are only several hundred to several thousand cm and the linewidths are only tens of cm it is necessary to use a monochromator with reasonably high resolution. In addition to linewidth issues, it is necessary to suppress the very intense Rayleigh scattering. If a high resolution spectrum is not needed, however, then it is possible to use narrow-band interference filters to block the excitation line, and a low resolution monocln-omator to collect the spectrum. In fact, this is the approach taken with Fourier transfonn Raman spectrometers. 

Once the basic work has been done, the observed spectrum can be calculated in several different ways. If the problem is solved in tlie time domain, then the solution provides a list of transitions. Each transition is defined by four quantities the mtegrated intensity, the frequency at which it appears, the linewidth (or decay rate in the time domain) and the phase. From this list of parameters, either a spectrum or a time-domain FID can be calculated easily. The spectrum has the advantage that it can be directly compared to the experimental result. An FID can be subjected to some sort of apodization before Fourier transfomiation to the spectrum this allows additional line broadening to be added to the spectrum independent of the sumilation. 

The potential of a tunable dye laser should not be overlooked. A tunable dye laser, employing an organic dye as lasing material allows one to choose any suitable excitation line within a particular region. This is in contrast to the case of a gas ion laser which has a limited number of emission lines at fixed wavelength. Nevertheless, a tunable dye laser has significant drawbacks such as poor resolution imposed by the dye laser linewidth (1.2 cm-1) and a continuous background spectrum which requires the use of a tunable filter 15-18). 

Fig. 12. Effect of a strong exchange interaction on the shape of the EPR spectrum displayed by a pair of centers A and B having identical g vEilues, = 1.89, g, = 1.96, g = 2.07, and rotated magnetic axes according to xjly, yglx, zJIzy,. (a) 9 GHz spectrum calculated with J = 0 (b) and (c) spectra calculated with J = 25 X 10 cm at 9 and 35 GHz, respectively. The spectra were calculated as described in Ref. 192) without including any dipolar terms, with the linewidths ui = cr, = oi = 0.01.

Optimum values for the probabilities may not be obtained in the case that experimental llnewidths in the spectrum are very different since only a single linewidth is used for the simulated spectra. The calculated probabilities may be stored in the database and hard copy reports may be printed-... 

Simulated spectra can be created by another option in the main menu of the program. Probabilities (P1-P4) are prompted from the user, depending on the model, if vaiues other than those stored with the data base are desired and a single linewidth is entered. Equation 1 and 2 are then used to simulate a spectrum which can be saved, compared to the experimental spectrum (including overlaying spectra, spectral subtractions, additions, etc.) or plotted. 

Once creation of the PV A database is complete, optimized probabilities may be calculated for the experimental spectrum at hand. Since the iterative procedure is restricted to a 2048 data point region, zoom cursors are displayed and set by the user until this condition is satisfied. In this case, the methylene region was selected and an initial guess for the Bernoullian probability (Pr=0.5) and linewidth (13.0Hz) were given. Optimized values for the probability and linewidth were Pr=0.52 and 12.8Hz, respectively. 

A portion of the database for this polymer is shown in Figure 6. Literature reports that this polymer follows second-order Markov statistics ( 21 ). And, in fact, probabilities that produced simulated spectra comparable to the experimental spectrum could not be obtained with Bernoullian or first-order Markov models. Figure 7 shows the experimental and simulated spectra for these ten pentads using the second-order Markov probabilities Pil/i=0.60, Piv/i=0.35, Pvi/i=0.40, and Pvv/i=0.55 and a linewidth of 14.8 Hz. 

Cosine smearing. Because instrument volume and experiment time must both be minimized for a planetary Mossbauer spectrometer, it is desirable in backscatter geometry to illuminate as much of the sample as possible with source radiation. However, this requirement at some point compromises the quality of the Mossbauer spectrum because of an effect known as cosine smearing [327, 348, 349] (see also Sects. 3.1.8 and 3.3). The effect on the Mossbauer spectrum is to increase the linewidth of Mossbauer peaks (which lowers the resolution) and shift their centers outward (affects the values of Mossbauer parameters). Therefore, the diameter of the source y-ray beam incident on the sample, which is determined by a... 

Fourier transformation without data manipulation leads to the multiplet at the bottom (a), which shows more fine structure when a negative LB value is used (b). The spectrum in the middle (c) results from use of the SSB function, and now all eight lines are clearly visible as the linewidth is much smaller. The price we pay is that the lineshape is completely changed, the positive central... 

The natural abundance of selenium-77 is 7.58%. The chemical shift of dimethyl selenide is set equal to 0 ppm. The total chemical shift range is around 2200 ppm, organoselenium compounds covering almost the whole range. Figure 41 shows the spectrum of H2Se03 in D20, the linewidth being only... 

Let us turn to the platinum spectra themselves. Figure 45 consists of three spectra. The top spectrum a shows the platinum signal from an inorganic salt, K2PtCl4. Note the linewidth of 45 Hz, relatively small in comparison with the... 

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